Looking at the wording it mentions walking down a London street.

Usually the press gangs would 'recruit' locally. The nearest navy dockyards to London in the 1800's when the press was really active were Deptford and Chatham.

So it is possible that this man in the song ended up in the Channel Fleet.

Unusual that they tied him by his thumbs. Normally a grating was used, this was rigged upright against the ships side and the man was triced up by his hands and feet. This ensured the boatswains mates, who carried out the flogging, had a steady target to strike at.

No mention of what the man was flogged for, but even things like spitting on the deck and not into a spitkid could earn a dozen lashes.

Technically any more than a dozen lashes would need a court marshal to decide the number to be given.

The man in the story does not sound like someone who had been to sea before so quite possibly this is based on a story about how a landsman or a waister got into trouble by breaking one or more of many rules and regulations that governed shipboard life.

The term waister was often applied to those with no sea experience. Their watch position would be in the waist of the ship between the quarterdeck and the forecastle. Here they were just expected to heave and pull on ropes and man the capstan. Until they gained more experience it was unusual to send them aloft.

Even in the modern navy a man with little experience or knowledge is still often referred as a bloody waister. A name tag often given to we naval apprentices when we were under training.